GAZA, March 18 (Reuters) - The Palestinian militant group Hamas on Tuesday called Egypt's curbs on movement through its crossing with the Gaza Strip a "crime against humanity", in an unprecedented rebuke of its Arab neighbour that further frays their worsening ties.

The closures, that Egypt says were introduced because of security concerns, have cut off imports of medicine and aid to the impoverished coastal enclave and prevented travel by thousands of Gazans and patients seeking treatment abroad.

Usually open for four to six days per month, the Rafah crossing has now been shut to normal passenger traffic for 40 straight days - although Egyptian authorities have opened it twice in that period for pilgims to Mecca.

"Egyptian authorities' insistence on closing the Rafah crossing and tightening the blockade of Gaza ... is a crime against humanity by every criteria and a crime against the Palestinian people," said Fawzi Barhoum, a spokesman for the Islamist movement which rules Gaza.

A Hamas official said on Tuesday Egypt had, for the first time, in the past few days cut off contacts with the Gaza government because of the dispute over the crossing, which Egyptian officials did not immediately confirm to Reuters.

Relations between Cairo and Gaza have steadily declined since Egypt's army ousted the country's first elected president, Islamist Mohamed Mursi, in July.

Hamas is an offshoot of Mursi's Muslim Brotherhood, which Egypt's military-backed government has declared a terrorist organisation.

Egypt has banned all Hamas activities in the country, accusing it of supporting an Islamist insurgency that has spread quickly, targeting security forces near daily, since Mursi's fall, allegations the Palestinian group denies.

An Egyptian security official told Reuters that security concerns dictate the status of the crossing and that they regularly open it for humanitarian reasons, such as for patients seeking treatment.

Egypt has also demolished hundreds of cross-border smuggling tunnels through which weapons, but also basic goods such as food and fuel, were transported into Gaza.

Israel has maintained strict curbs on the movement of goods and people in Gaza since Hamas took control there following bloody battles with Palestinian rivals in 2007.

The twin blockades have left the Gaza Strip's industry and construction sectors gasping for resources, pushing unemployment to new lows and deepening poverty.